Consulting services are provided to NIH researchers in a variety of disciplines including physics, applied mathematics, and statistics. A theory has been developed for the calculation of sampling errors in kinetics experiments. Two variants of the theory have been applied, one to parameters measured in the use of positron emission tomography, and the second to errors incurred in Fourier transform NMR spectroscopy. In the first of these applications the techniques allow estimation of experimental error from available data, but will also furnish a means of optimizing the use of PET scanners. In the second, we have compared the accuracy and precision of peak area estimates obtained by curve fitting and numerical integration from FT NMR data. Both methods are currently used by NMR spectroscopists, but our analysis showed that curve fitting is far superior to numerical integration. A joint study of the validity of the Wilemski-Fixman approximation for calculations of rates in polymer physics is presently underway with A. Szabo. Calculations with an exactly solvable model allow us to estimate the limits of validity of this model, and integral equation methods have suggested more accurate alternatives to the much used approximation. Together with J. Aron we have developed a mathematical model of the kinetics of diseases with superinfection. A joint project has been initiated on the understanding of the kinetics of diffusion-controlled reactions. Approximate techniques for the solution of such problems in polymer physics have been in the literature for many years. An application of infinite order perturbation theory techniques has led to an understanding of limitations on present approximations and to improvements in the calculation of rates.